In order to analyze the supersonic and transonic panel flutter behaviors quantitatively and accurately, a fluid-structure coupling algorithm based on the finite element method (FEM) is proposed to study the two-dimensional panel flutter problem. First, the Von Kármán's large deformation is used to model the panel, and the high speed airflow is approached by the Euler equations. Then, the equation of panel is discretized spatially by the standard Galerkin FEM, and the equations of fluid are discretized by the characteristic-based split finite element method (CBS-FEM) with dual time stepping; thus, the numerical oscillation encountered frequently in the numerical simulation of flow field could be removed efficiently. Further, a staggered algorithm is used to transfer the information on the interface between the fluid and the structure. Finally, the aeroelastic behaviors of the panel in both the supersonic and transonic airflows are studied in details. And the results show that the system can present the flat and stable, simple harmonic oscillation, buckling, and inharmonic oscillation states at Mach 2, considering the effect of the pretightening force; at Mach 1.2, as the panel loses stability, the ensuing limit cycle oscillation is born; at Mach 0.8 and 0.9, positive and negative bucklings are the typical states of the panel as it loses its stability. Further, the transonic stability boundary is obtained and the transonic bucket is precisely captured. More, this algorithm can be applied to the numerical analysis of other complicated problems related to aeroelasticity.

References

References
1.
Dowell
,
E. H.
,
1975
,
Aeroelasticity of Plates and Shells
,
Noordhoff
,
Groningen
, Netherlands.
2.
Dowell
,
E. H.
,
2005
,
A Modern Course in Aeroelasticity
,
Kluwer
,
New York
.
3.
Kang
,
W.
,
Zhang
,
J. Z.
, and
Feng
,
P. H.
,
2012
, “
Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers
,”
Commun. Comput. Phys.
,
11
(
4
), pp.
1300
1310
10.4208/cicp.070510.150511s.
4.
Dowell
,
E. H.
,
1966
, “
Nonlinear Oscillations of a Fluttering Plate
,”
AIAA J.
,
4
(
7
), pp.
1267
1275
.10.2514/3.3658
5.
Dowell
,
E. H.
,
1967
, “
Nonlinear Oscillations of a Fluttering Plate II
,”
AIAA J.
,
5
(
10
), pp.
1856
1862
.10.2514/3.4316
6.
Dowell
,
E. H.
,
1970
, “
A Review of the Aeroelastic Stability of Plates and Shells
,”
AIAA J.
,
8
(
1
), pp.
385
399
.10.2514/3.5680
7.
Olson
,
M. D.
,
1967
, “
Finite Element Approach to Panel Flutter
,”
AIAA J.
,
5
(
12
), pp.
226
227
.10.2514/3.3946
8.
Olson
,
M. D.
,
1970
, “
Some Flutter Solutions Using Finite Element
,”
AIAA J.
,
8
(
4
), pp.
747
752
.10.2514/3.5751
9.
Mei
,
C. H.
,
Abdel-Motagly
,
K.
, and
Chen
,
R.
,
1999
, “
Review of Nonlinear Panel Flutter at Supersonic and Hypersonic Speeds
,”
ASME Appl. Mech. Rev.
,
52
(
10
), pp.
321
332
.10.1115/1.3098919
10.
Cheng
,
G. F.
, and
Mei
,
C. H.
,
2004
, “
Finite Element Modal Formulation for Hypersonic Panel Flutter Analysis With Thermal Effects
,”
AIAA J.
,
42
(
4
), pp.
687
695
.10.2514/1.9553
11.
Ashley
,
H.
, and
Zartarian
,
G.
,
1956
, “
Piston Theory—A New Aerodynamic Tool for the Aeroelastician
,”
J. Aeronaut. Sci.
,
23
(
12
), pp.
1109
1118
.10.2514/8.3740
12.
Zhang
,
W. W.
,
Ye
,
Z. Y.
,
Zhang
,
C. A.
, and
Liu
,
F.
,
2009
, “
Supersonic Flutter Analysis Based on a Local Piston Theory
,”
AIAA J.
,
47
(
10
), pp.
2321
2328
.10.2514/1.37750
13.
Davis
,
G. A.
, and
Bendiksen
,
O. O.
,
1993
, “
Unsteady Transonic Two-Dimensional Euler Solutions Using Finite Elements
,”
AIAA J.
,
31
(
6
), pp.
1051
1059
.10.2514/3.11728
14.
Davis
,
G. A.
,
1994
, “
Transonic Aeroelasticity Solutions Using Finite Elements in an Arbitrary Larangian-Eulerian Formulation
,” Ph.D. thesis, University of California, Los Angeles, CA.
15.
Gordiner
,
R. E.
, and
Fithen
,
R.
,
2003
, “
Coupling of a Nonlinear Finite Element Structural Method With a Navier–Stokes Solver
,”
Comput. Struct.
,
81
(
2
), pp.
75
89
.10.1016/S0045-7949(02)00390-5
16.
Hashimoto
,
A.
, and
Aoyama
,
T.
,
2009
, “
Effects of Turbulent Boundary Layer on Panel Flutter
,”
AIAA J.
,
47
(
12
), pp.
2785
2791
.10.2514/1.35786
17.
Mublstein
,
L.
,
Gaspers
,
P. A.
, and
Riddle
,
D. W.
,
1968
, “
An Experimental Study of the Influence of the Turbulent Boundary Layer on Panel Flutter
,” NASA Paper No. TN D–4486.
18.
Zhang
,
J. Z.
,
Ren
,
S.
, and
Mei
,
G. H.
,
2011
, “
Model Reduction on Inertial Manifolds for N-S Equations Approached by Multilevel Finite Element Method
,”
Commun. Nonlinear Sci. Numer. Simulation
,
16
(
1
), pp.
195
205
.10.1016/j.cnsns.2010.02.023
19.
Zienkiewicz
,
O. C.
,
Taylor
,
R. L.
, and
Nithiarasu
,
P.
,
2009
,
The Finite Element Method for Fluid Dynamics
,
6th ed.
,
Elsevier
,
Singapore
.
20.
Wang
,
Y. T.
, and
Zhang
,
J. Z.
,
2011
, “
An Improved ALE and CBS-Based Finite Element Algorithm for Analyzing Flows Around Forced Oscillating Bodies
,”
Finite Elements Anal. Des.
,
47
(
9
), pp.
1058
1065
.10.1016/j.finel.2011.03.021
21.
Sun
,
X.
,
Zhang
,
J. Z.
, and
Ren
,
X. L.
,
2012
, “
Characteristic-Based Split (CBS) Finite Element Method for Incompressible Viscous Flow With Moving Boundaries
,”
Eng. Appl. Comput. Fluid Mech.
,
6
(
3
), pp.
461
474
.
22.
Massarotti
,
N.
,
Arpino
,
F.
,
Lewis
,
R. W.
, and
Nithiarasu
,
P.
,
2006
, “
Explicit and Semi-Implicit CBS Procedures for Incompressible Viscous Flows
,”
Int. J. Numer. Methods Eng.
,
66
(
10
), pp.
1618
1640
.10.1002/nme.1700
23.
Nithiarasu
,
P.
,
Mathur
,
J. S.
,
Weatherill
,
N. P.
, and
Morgan
,
K.
,
2004
, “
Three-Dimensional Incompressible Flow Calculations Using the Characteristic Based Split (CBS) Scheme
,”
Int. J. Numer. Methods Fluids
,
44
(
11
), pp.
1207
1229
.10.1002/fld.682
24.
Nithiarasu
,
P.
,
2003
, “
An Efficient Artificial Compressibility (AC) Scheme Based on the Characteristic Based Split (CBS) Method for Incompressible Flows
,”
Int. J. Numer. Methods Eng.
,
56
(
13
), pp.
1815
1845
.10.1002/nme.712
25.
Nithiarasu
,
P.
,
Zienkiewicz
,
O. C.
,
SatyaSai
,
B. V. K.
,
Morgan
,
K.
,
Codina
,
R.
, and
Vazquez
,
M.
,
1998
, “
Shock Capturing Viscosities for the General Fluid Mechanics Algorithm
,”
Int. J. Numer. Methods Eng.
,
28
(
9
), pp.
1325
1353
.10.1002/(SICI)1097-0363(19981215)28:9<1325::AID-FLD765>3.0.CO;2-1
26.
Thomas
,
J. L.
, and
Salas
,
M. D.
,
1986
, “
Far-Field Boundary Conditions for Transonic Lifting Solutions to the Euler Equations
,”
AIAA J.
,
24
(
7
), pp.
1074
1080
.10.2514/3.9394
27.
Kamakoti
,
R.
, and
Shyy
,
W.
,
2004
, “
Fluid-Structure Interaction for Aeroelastic Applications
,”
Prog. Aerosp. Sci.
,
40
(
8
), pp.
535
558
.10.1016/j.paerosci.2005.01.001
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